Representations and Modules of Rota-Baxter Algebras
Li Guo, Zongzhu Lin

TL;DR
This paper provides a comprehensive study of the representation and module theory of Rota-Baxter algebras, including decompositions, categorical equivalences, and applications to coalgebras and tensor categories.
Contribution
It introduces new structures and equivalences in Rota-Baxter algebra representations, including regular-singular decompositions and categorical frameworks.
Findings
Decomposition of Rota-Baxter algebras and modules under quasi-idempotency
Equivalence between Rota-Baxter algebra representations and Rota-Baxter operator ring representations
Explicit constructions and algebraic Birkhoff factorization in coalgebra representations
Abstract
We give a broad study of representation and module theory of Rota-Baxter algebras. Regular-singular decompositions of Rota-Baxter algebras and Rota-Baxter modules are obtained under the condition of quasi-idempotency. Representations of an Rota-Baxter algebra are shown to be equivalent to the representations of the ring of Rota-Baxter operators whose categorical properties are obtained and explicit constructions are provided. Representations from coalgebras are investigated and their algebraic Birkhoff factorization is given. Representations of Rota-Baxter algebras in the tensor category context is also formulated.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Matrix Theory and Algorithms
